Assessed value = never been to your property, an equation gives you this number.
Market value = what someone will pay for your home (as you mention). The city may miss key features to your property or development without permits may be done adding value that the city is not aware of (also can decrease value in some buyers eyes)

I have sold homes for 100k+/- the city assessed value. There is no real standard and it is why I almost never use them when determining the value of a home. The only time a buyer or seller ever uses the city assessment argument is when it is in their favor which should tell you that it is not a good indicator!